How to create a buffered pH gradient?

Hey! I've been working on this problem - I think it would be easy for a chemist to answer. If anyone can help me out, I'd appreciate it!

Suppose I want to create a pH gradient from 3 to 9, in increments of 0.5:

pH = (3, 3.5, 4, 4.5, 5, 5.5, 6, 6.5, 7, 7.5, 8, 8.5, 9)

Each pH is in a different test tube. I also want to buffer the pH in each test tube. Therefore, in the pH=4 test tube, I would use a buffer with a pKa~4, and in the pH=8 test tube, I would use a buffer with a pKa~8. However, it's important that I construct this gradient in such a way that aside from pH, everything else is held constant. In other words, if I add a phosphate buffer to one test tube, it would be best if I could add the same amount of phosphate to all test tubes.

Therefore, I was hoping I could use a mixture of buffers with different pKas. Each test tube would have every buffer, and to adjust the pH, I would only vary the amount of HCl I add to the solution. The idea is that different buffers will be active in different test tubes, depending on the amount of HCl I add.

So my main question is: *Is this possible?* I was also curious if anyone knows how to calculate the pH of a multi-buffered solution like this? Is there an extension of the Henderson-Hasselbalch equation I can use?

I could also look at buffers that have multiple dissociation constants. For example, phosphate buffer has pKas at 2.15, 6.86 and 12.32. This exceeds the range I am interested in, but perhaps there is another buffer that I could use? Just a thought.

Staff: Mentor

Definitely possible, although not easy. You need to use several weak acids (preferably multiprotic) to cover as wide pH range as possible. For pH between 3 and 6 citric acid is perfect, I can't think of any single acid that would work for pH 6 to 9 range. Pyrophosphoric perhaps? In general I would look for something with pKa around 7.5 (like TAPSO, Triethanolamine or N-Ethylmorpholine) and something with pKa around 9 (Bis-Tris propane). Plenty of combinations to test.

These are not things that you can calculate with HH equation. But it is exactly kind of task that Buffer Maker was written for. It would be also perfect to test all these combinations I have mentioned above.

Thanks for the quick reply! Your response helped a lot. Do you know if a program like Buffer Maker is available for Mac or GNU/Linux?

I have read a little about "universal buffers" which can give large pH ranges. The example in Wikipedia is McIlvaine's buffer solutions (Na2HPO4 and Citric Acid), which give pH 3-8.

The problem is that they require varying amounts of Na2HPO4 and Citric Acid. Ideally, I would keep the concentrations of all the buffers the same and only vary the amount of HCl.

Just to be clear, it sounds like you're suggesting I choose a slightly more complex mixture of buffers, keep their concentrations the same in all test tubes, and only vary HCl? Sorry! I'm just learning everything, so it might take me a while to catch on :) Thanks again!

Staff: Mentor

Buffer Maker has only Windows version, and I am not aware of any other similar program for other platforms.

Instead of using Na2HPO4 and citric acid you can use H3PO4 and citric acid and vary amount of NaOH used to neutralize the mixture. This way total concentrations of phosphates and citrates stays the same. Same can be said about any other mixture. This is more or less equivalent to your idea of varying amount of HCl added, just if you start with citric acid it is a strong base that makes more sense.

Thanks again. I think I'm beginning to understand :) Now this might be a dumb question...

If I look at a citric acid/H3PO4 mixture, the pKas are 3, 5, and 6.5 (for citric acid) and 2, 7, and 12 (phosphate). Maybe I am missing something, but it seems this mixture is missing a buffer in the 8-12 range? Therefore, would it be a poor buffer for pH 8-12?

Would you suggest adding yet another component (such as boric acid or Bis-Tris propane)?

The Buffer Maker program looks really useful! I'll try to get a hold of a Windows computer to use it. Thanks!

I have heard of these universal buffers and either forgot or never knew much about them. Why do you want to keep the concentration constant? I wonder what is influenced by this concentration such that you want to keep it constant. For if phosphate concentration is constant over the pH range, the concentrations of the different ionic species cannot be. Nor, what may be more important, is the ionic strength. To make it more difficult some of the buffers suggested may have multiple charges - phosphate, pyrophosphate, citrate, so strong ionic strength (proportional to charge2) effects.

Depending on what your overall problem is, one possible solution is to use simple buffer species you hope will not interact with whatever else is important in your system, as dilute as possible and have sufficient salt, NaCl, that it dominates the ionic strength. Another way, if you are e.g. expecting a chemical reaction that can change the pH you want constant, is to use a pH-stat machine that adds acid or alkali such as to keep pH constant. (That can also be a way to measure the reaction.) Again a sufficient NaCl concentration is preferable or essential.

It is quite a difficult problem and an answer would depend on what really you are trying to do.

Staff: Mentor

For if phosphate concentration is constant over the pH range, the concentrations of the different ionic species cannot be. Nor, what may be more important, is the ionic strength.

It is possible to construct a buffer that keeps ionic strength constant in some pH range (the idea is to use at least two acid/base pairs, so that changes in ionic strength of one pair are compensated by changes in the other), but I am not aware of any that will work in that wide range.

I have obtained and read the publication by Elving et al in Analytical Chemistry, Vol. 28 #7, pages 1179-1180 (1956). In that publication they list formulas for mixing the Citric acid and Na2HPO4 solutions to prepare the various pH buffers. They are basically using the identical ratios of these two components originally proposed by McIlvaine in J. Biol. Chem. Vol. 49, pages 183-186 (1921). I have checked these calculations and they are correct. What I can't figure out is how to verify their values of ionic strength list in Table 1 of the Elving et al, publication. Any help is most appreciated.
P.S. I cannot get Buffer Maker program to work

Staff: Mentor

I have checked these calculations and they are correct. What I can't figure out is how to verify their values of ionic strength list in Table 1 of the Elving et al, publication.

I don't see how you could be able to check that the calculations are correct and yet be not able to check the ionic strength. If you don't know the ionic strength, you can't get correct results of the calculations.

Please keep your discussion in the original thread you started for that purpose.

What kind of problems do you have with the Buffer Maker? Have you tried to contact support?

I guess we have already given the best help we can - especially as we don't know what you are trying to do!

There can't be many biological/biochemical problems that you have to investigate over a pH range from 3 to 9.

But anyway it sounds like something that varies with pH but you are afraid that any effects you get of pH are influenced not by pH alone, but by concentrations of other ions - the general ionic atmosphere. I guess you can do the best you can to minimise though not be really sure you have totally eliminated it by your approach of buffer selection. One reason this is bit rough IMO is that the concept of the ionic strength so far as I know comes out of the Debye-Huckel theory - which is supposed to be only good up to 10-3 M or still less. With these polyions you have quite non ideal solutions, you can't be totally sure what you doing IMHO.

So the only rigorous approach I see to keeping these ionic atmosphere effects constant are the ones I suggested before - use minimum buffer concentration possible, and make the major ionic strength contribution come from a neutral salt like NaCl, or use a pH-stat.